Navigational Decision Making in Drosophila Thermotaxis

Statistics of runs and turning events during positive thermotaxis. A, Representative trajectory of a wild-type larva crawling up a linear thermal gradient (0.5°C/cm steepness, 17.5°C start temperature) depicting the characteristic sequence of straight runs interrupted by turning events. The zoomed inset shows a portion of the trajectory, highlighting a series of distinct runs and seven turning events (indicated by letters a–g). For presentation purposes, we use a quadrant color code to distinguish runs with different headings relative to 0°, the direction of the temperature gradient. Red, Runs pointed toward warmer temperatures with headings between −45° and +45°. Orange, Transverse runs with headings between +45° and +135°. Green, Transverse runs with headings between −45° and −135°. Blue, Runs pointed toward colder temperatures with headings >135° or <−135°. No runs in the zoomed inset happen to be toward colder temperatures. For the representative turning event indicated by the letter f, a series of video frames reveal the details of the larva's head sweeps: the first head sweep is to the larva's left, the second head sweep is to the larva's right, and the new run is initiated with a heading change of −83.0° with respect to the previous run. B–G, Statistics of runs and turning events exhibited by wild-type larvae performing positive thermotaxis when navigating linear spatial thermal gradients (0.5°C/cm; 17.5°C start temperature). Statistics represent the trajectories of 21 animals, separated into 785 discrete runs, with a turning event at the start and end of each run. All data points are colored on the basis of run direction using the quadrant color code described in A. B, Scatter plot showing the temporal duration of each run with respect to the mean heading of each run. C, Distribution of the durations of all runs pointed up the gradient (red) and down the gradient (blue) using the measurements shown in B. Solid lines and time constants correspond to exponential fits to each distribution. **The time constants of the exponential fits are significantly different at p < 0.005 using the two-sample Kolmogorov Smirnov test. D, Crawling speed during runs as a function of run heading. Each data point represents mean ± 1 SE. E, Distribution of the number of runs that were exhibited at different headings taken from all trajectories. Error bars represent 1 SE. F, Scatter plots and histograms of heading changes between the start and end of each run as a function of the initial heading of the run. The heading change by the end of each run is calculated using the compass shown in A: negative and positive values correspond to rightward and leftward heading changes, respectively, from the larva's point of view. Scatter plots (bottom) depict all measured heading changes during each run, separated into quadrants depending on the initial heading of each run. Histograms of these measurements (top), show the probability distributions of heading changes, and each solid line is a fit to the normal distribution. The mean and the SD in each heading change distribution, shown above each histogram, are indistinguishable from one another at p > 0.05, using Student's t test to compare means and the F test to compare variances. G, Statistics of heading changes generated by each turning event as a function of the run heading immediately before the turning event. Negative and positive heading changes correspond to rightward and leftward turns, respectively, from the larva's point of view. Scatter plots (bottom) depict all measured turning events, separated into quadrants depending on the run heading immediately before each turning event. Histograms of these measurements (top) show the probability distributions of heading changes. The mean and SD for each heading change distribution is shown above each histogram. **Cases in which the mean or the SD in the heading change distribution for each quadrant differed from those values for the quadrant in which larvae crawled up the temperature gradient (red data points) at p < 0.005 using Student's t test to compare means and F test to compare variances.

Genetic disruption of the cold-sensitive neurons in the terminal organ. A–C, Representative trajectories of first instar larvae navigating linear spatial thermal gradients (0.5°C/cm; 17.5°C start temperatures) on the surface of 9 cm diameter agar plates. A, GH86-Gal4 larvae (n = 46) crawl up the temperature gradient with thermotactic index of 0.8 ± 0.1. B, UAS-TNT-E larvae (n = 50) crawl up the temperature gradients with thermotactic index of 0.7 ± 0.1. C, GH86-Gal4/Y or +; +/UAS-TNT-E larvae (n = 111) have significantly diminished preference for warmer temperatures with thermotactic index of 0.3 ± 0.1 (p < 0.005 difference from either GH86-Gal4 larvae or UAS-TNT-E larvae using Student's t test). D–L, The statistics of run and turning behavior taken from all the trajectories exhibited by individual mutant larvae as shown in Figure 2 for wild-type larvae: GH86-Gal4 (n = 46 animals separated into 705 discrete runs) (D, G, J); UAS-TNT-E (n = 50 animals separated into 1230 discrete runs) (E, H, K); or GH86>TNT-E (n = 111 animals separated into 3525 discrete runs) (F, I, L). For presentation purposes, we use the quadrant color code shown in Figure 2A to distinguish runs with different headings with respect to 0°, the direction of the temperature gradient: red corresponds to runs pointed toward warmer temperatures with headings between −45° and +45°; orange corresponds to transverse runs with headings between +45° and +135°; green corresponds to transverse runs with headings between −45° and −135°; blue corresponds to runs pointed toward colder temperatures with headings >135° or <−135°. D–F, Distribution of the durations of all runs pointed up and down each temperature gradient for each strain. Solid lines and time constants correspond to exponential fits for runs pointed toward warmer or colder temperatures, and ** in each figure indicates cases in which the two time constants differ at p < 0.005 using the two-sample Kolmogorov–Smirnov test. G–I, Distribution of the numbers of runs with different run headings taken from the all trajectories exhibited by each strain. J–L, Histograms of heading changes after each turning event taken from all trajectories for each mutant strain. Data are separated into quadrants depending on run heading before each turning event. Asterisks indicate cases in which the mean or the SD in the heading change distribution for each quadrant differed from those values for the quadrant in which larvae crawled up the temperature gradient (*p < 0.05; **p < 0.005 using Student's t test to compare means and the F test to compare variances).

Statistics of head sweeps during turning events. A, The distribution of the number of head sweeps per turning event during positive thermotaxis exhibited by wild-type larvae (n = 21 animals, 785 turning events); GH86-Gal4 larvae (n = 46 animals, 705 turning events); UAS-TNT-E larvae (n = 50 animals, 1230 turning events); and GH86>TNT-E larvae (n = 111 animals, 3525 turning events). B, The probability that the first head sweep in each turning event is toward warmer temperatures following runs transverse to the temperature gradient. In every case, the probability was statistically indistinguishable from 50% (p > 0.05 using a one-sample Z test). C, The probability that the larva ends a turning event and starts a new run during head sweeps toward warmer temperatures (red bars) or during head sweeps toward colder temperatures (blue bars) for turning events following runs transverse to the temperature direction. **Cases in which these two probabilities for wild-type or mutant larvae differ at p < 0.005 using a two-sample Z test. D, The maximum extent of head sweeps during each turning event (i.e., the largest absolute value of the angle between head and body) of mutant and wild-type larvae depending on the initial heading of the larvae with respect to the temperature gradient before each turning event separated into quadrants. For each strain, ** indicates cases in which the maximum extent of head sweeps for each quadrant differed from the value for the quadrant in which larvae crawled up the temperature gradient at p < 0.005 using Student's t test.

Statistics of runs, turns, and head sweeps during negative thermotaxis. A, For presentation purposes, we use a quadrant color code to distinguish runs with different headings with respect to 0°: blue corresponds to runs pointed toward colder temperatures with headings between −45° and +45°; orange corresponds to transverse runs with headings between +45° and +135°; green corresponds to transverse runs with headings between −45° and −135°; red corresponds to runs pointed toward warmer temperatures with headings >135° or <−135°. B–K, Statistics of runs, turns, and head sweeps exhibited by wild-type larvae performing negative thermotaxis when navigating linear spatial thermal gradients (0.5°C/cm; 40°C start temperature). Statistics represent the trajectories of 57 animals, separated into 492 discrete runs, with a turning event at the start and end of each run. All data points are colored on the basis of run direction using the quadrant color code of Figure 5A. B, Scatter plot showing the temporal duration of each run with respect to the mean heading of each run. C, Distribution of the durations of all runs pointed up the gradient (red) and down the gradient (blue) using the individual measurements shown in B. Solid lines and time constants correspond to exponential fits to each distribution. **The time constants of the exponential fits are statistically distinguishable at p < 0.005 using the two-sample Kolmogorov Smirnov test. D, Crawling speed during runs as a function of run heading. Each data point represents mean ± 1 SE. E, Distribution of the number of runs that were exhibited at different headings taken from all trajectories. Error bars represent 1 SE. F, Scatter plots and histograms of heading changes between the start and end of each run as a function of the initial heading of the run. The heading change by the end of each run is calculated using the compass shown in Figure 5A: negative and positive values correspond to leftward and rightward heading changes, respectively, from the larva's point of view. Scatter plots (bottom) depict all measured heading changes during each run, separated into quadrants depending on the initial heading of each run. Histograms of these measurements (top), show the probability distributions of heading changes, and each solid line is a fit to the normal distribution. The mean and the SD in each heading change distribution, shown above each histogram, are indistinguishable from one another at p > 0.05 using Student's t test to compare means and F test to compare variances. G, Statistics of heading changes generated by each turning event as a function of the run heading immediately before the turning event. Negative and positive heading changes correspond to leftward and rightward turns, respectively, from the larva's point of view. Scatter plots (bottom) depict all measured turning events, separated into quadrants depending on the run heading immediately before each turning event. Histograms of these measurements (top) show the probability distributions of heading changes. The mean and SD for each heading change distribution is shown above each histogram. Asterisks indicate cases in which the mean or the SD in the heading change distribution for each quadrant differed from those values for the quadrant in which larvae crawled up the temperature gradient (*p < 0.05, **p < 0.005 using Student's t test to compare means and F test to compare variances). H, The distribution of the number of head sweeps per turning event during negative thermotaxis. I, The probability that the first head sweep in each turning event is toward warmer temperatures following runs transverse to the temperature gradient. The probability was statistically indistinguishable from 50% at p > 0.05 using the one-sample Z test. J, The probability that the larva ends a turning event and starts a new run during head sweeps toward warmer temperatures (red bars) or during head sweeps toward colder temperatures (blue bars) for turning events after runs transverse to the temperature direction. **Cases in which these two probabilities differ at p < 0.005 using the two-sample Z test. K, The maximum extent of head sweeps during each turning event (i.e., the largest absolute value of the angle between head and body) depending on the initial heading of the. **Cases in which the maximum extent of head sweeps for each quadrant differed from the value for the quadrant in which larvae crawled up the temperature gradient at p < 0.005 using Student's t test.

Temporal gradients evoke thermotactic behavior. A–D, Individual larvae were placed on agar plates and subjected to spatially uniform temporal gradients of temperature, delivered in the temperature cycles between 16 and 17°C with 1°C/min ramp speed and 2 min period as shown in A. Statistics represent measurements taken from n = 42 larvae exhibiting a total of 562 runs. B, The mean durations of all runs exhibited during the warming and cooling phases. **The mean durations differed at p < 0.005 using Student's t test. C, The histogram of heading changes effected by each turn during the warming phase (red dots) and during the cooling phase (blue dots). Lines show fits to normal distributions, and each SD corresponds to the width of each normal distribution. **The two SDs differ at p < 0.005 using the F test. D, Distribution of the number of head sweeps that larvae use to effect each turn during the warming phases (red bars) and cooling phases (blue bars) of the temperature ramps. **The mean number of head sweeps per turning event during the warming and cooling phases differ at p < 0.005 using Student's t test. E–H, Individual larvae were placed on agar plates and subjected to spatially uniform temporal gradients of temperature, delivered in the temperature cycles between 38 and 39°C with 1°C/min ramp speed and 2 min period as shown in E. Statistics represent measurements taken from n = 128 larvae exhibiting a total of 1099 runs. F, The mean durations of all runs exhibited during the warming and cooling phases. **The mean durations differed at p < 0.005 using Student's t test. G, The histogram of heading changes effected by each turn during the warming phase (red) and during the cooling phase (blue). Lines show fits to normal distributions, and each SD corresponds to the width of each normal distribution. **The two SDs differ at p < 0.005 using the F test. H, Distribution of the number of head sweeps that larvae use to effect each turn during the warming phases (red bars) and cooling phases (blue bars) of the temperature ramps. **The mean number of head sweeps per turning event during the warming and cooling phases differ at p < 0.005 using Student's t test.

Heating or cooling during head sweeps regulates turning decisions during positive thermotaxis. A, Video images of an individual wild-type larva navigating an agar surface held at 17°C. The larva is entrained with an infrared laser spotlight that switches on during certain head sweeps. At t = 0 s, the larva is exhibiting a run with the laser off. At t = 9 s, the larva has spontaneously initiated a turning event, in which the first head sweep is to the larva's right and the laser stays off. The larva does not initiate a new run during the first head sweep, and at t = 12 s the larva's head returns to the centerline. At t = 14 s, the larva initiates a second head sweep to its left. During the second head sweep, the laser turns on (indicated by the red background), and the larva initiates a new run. At t = 33 s, the larva is exhibiting its new run in its new orientation after the turning event. B, The probability that larvae start new runs during head sweeps as they navigate agar surfaces held at 17°C with illumination from an infrared laser spotlight that depends on head sweeps. In one set of experiments as depicted in Figure 5E (red bars), the laser was kept off during runs, and was either switched on during a head sweep to warm the larva (filled red bar) or was kept off during a head sweep to maintain constant temperature (open red bar). **The probability of ending the turning event during head sweeps when the larva experienced warming differed from the probability of ending the turning event during head sweeps when the larva experienced no temperature change at p < 0.005 using Student's t test. In another set of experiments (blue bars), the laser was kept on during runs, and was either switched off during a head sweep to cool the larva (filled blue bar) or was kept on during a head sweep to maintain constant temperature (open blue bar). **The probability of ending the turning event during head sweeps when the larva experienced cooling differed from the probability of ending during head sweeps when the larva experienced no temperature change at p < 0.005 using Student's t test.

Simulations of thermotactic navigation. A–E, Monte Carlo simulations of the trajectories of larvae exhibiting positive thermotaxis using the statistical distributions for run duration, turn size, and turn direction exhibited by real larvae navigating 0.5°C/cm temperature gradients with 17.5°C start temperature. For wild-type larvae, each of these statistical distributions is explicitly dependent on the larva's heading as described in Figure 2. To simulate the effect of negating specific aspects of behavioral strategy, we constructed a set of unbiased statistical distributions for run duration, turn size, and turn direction by pooling all run and turn statistics exhibited by wild-type larvae without separation into quadrants based on run heading. A–C, Simulated trajectories of larvae regulating only one aspect of behavioral strategy. In each case, we allowed the simulated larva's heading to generate the statistics for one aspect of behavioral strategy using the statistical distributions exhibited by real larvae, and used unbiased statistical distributions for the other two aspects of behavioral strategy. In each panel, the trajectories produced by 30 simulations are superposed (purple trajectories), and two randomly selected trajectories are highlighted in blue and red. D, Simulated trajectories of larvae that use all three wild-type distributions for run duration, turn size, and turn direction. E, Thermotactic movement of simulations with zero, one, two, or all three types of modulation of run and turning behavior, quantified as the mean drift velocity of each simulation as it crawls up temperature gradients. As expected, simulations with zero bias exhibit zero drift velocity. For comparison, the experimentally measured drift speed of wild-type larvae exhibiting positive thermotaxis is indicated in red. Each measurement represents the mean ± 1 SE. F, Results of Monte Carlo simulations of the trajectories of larvae exhibiting negative thermotaxis using the statistical distributions for run duration, turn size, and turn direction exhibited by real larvae navigating 0.5°C/cm temperature gradients with 40°C start temperature taken from Figure 5. As in E, thermotactic movement of simulations with zero, one, two, or all three types of modulation of run and turning behavior is quantified as the mean drift velocity of each simulation as it crawls down temperature gradients. For comparison, the experimentally measured drift speed of wild-type larvae exhibiting negative thermotaxis is indicated in red. Each measurement represents the mean ± 1 SE.